t-SNE projections in MATLAB^®

How to make t-SNE projections in MATLAB^® with Plotly.

Visualize Fisher Iris Data

The Fisher iris data set has four-dimensional measurements of irises, and corresponding classification into species. Visualize this data by reducing the dimension using tsne.

load fisheriris
rng default % for reproducibility
Y = tsne(meas);
gscatter(Y(:,1),Y(:,2),species)

fig2plotly(gcf);

Compare Distance Metrics

Use various distance metrics to try to obtain a better separation between species in the Fisher iris data.

load fisheriris

rng('default') % for reproducibility
Y = tsne(meas,'Algorithm','exact','Distance','mahalanobis');
subplot(2,2,1)
gscatter(Y(:,1),Y(:,2),species)
title('Mahalanobis')

rng('default') % for fair comparison
Y = tsne(meas,'Algorithm','exact','Distance','cosine');
subplot(2,2,2)
gscatter(Y(:,1),Y(:,2),species)
title('Cosine')

rng('default') % for fair comparison
Y = tsne(meas,'Algorithm','exact','Distance','chebychev');
subplot(2,2,3)
gscatter(Y(:,1),Y(:,2),species)
title('Chebychev')

rng('default') % for fair comparison
Y = tsne(meas,'Algorithm','exact','Distance','euclidean');
subplot(2,2,4)
gscatter(Y(:,1),Y(:,2),species)
title('Euclidean')

fig2plotly(gcf);

In this case, the cosine, Chebychev, and Euclidean distance metrics give reasonably good separation of clusters. But the Mahalanobis distance metric does not give a good separation.

Plot Results with NaN Input Data

tsne removes input data rows that contain any NaN entries. Therefore, you must remove any such rows from your classification data before plotting.

For example, change a few random entries in the Fisher iris data to NaN.

load fisheriris
rng default % for reproducibility
meas(rand(size(meas)) < 0.05) = NaN;

Embed the four-dimensional data into two dimensions using tsne.

load fisheriris;
rng default; % for reproducibility
meas(rand(size(meas)) < 0.05) = NaN;

Y = tsne(meas,'Algorithm','exact');

[Warning: Rows with NaN missing values in X or 'InitialY' values are removed.] 
[> In line 65)]

Determine how many rows were eliminated from the embedding.

load fisheriris;
rng default; % for reproducibility
meas(rand(size(meas)) < 0.05) = NaN;

Y = tsne(meas,'Algorithm','exact');

length(species)-length(Y)

[Warning: Rows with NaN missing values in X or 'InitialY' values are removed.] 
[> In line 65)] 

ans =

    22

Prepare to plot the result by locating the rows of meas that have no NaN values.

load fisheriris;
rng default; % for reproducibility
meas(rand(size(meas)) < 0.05) = NaN;

goodrows = not(any(isnan(meas),2));

Plot the results using only the rows of species that correspond to rows of meas with no NaN values.

load fisheriris;
rng default; % for reproducibility
meas(rand(size(meas)) < 0.05) = NaN;

Y = tsne(meas,'Algorithm','exact');

goodrows = not(any(isnan(meas),2));

gscatter(Y(:,1),Y(:,2),species(goodrows))

fig2plotly(gcf);

[Warning: Rows with NaN missing values in X or 'InitialY' values are removed.] 
[> In line 65)]

Compare t-SNE Loss

Find both 2-D and 3-D embeddings of the Fisher iris data, and compare the loss for each embedding. It is likely that the loss is lower for a 3-D embedding, because this embedding has more freedom to match the original data.

load fisheriris;
rng default; % for reproducibility
[Y,loss] = tsne(meas,'Algorithm','exact');
rng default % for fair comparison
[Y2,loss2] = tsne(meas,'Algorithm','exact','NumDimensions',3);
fprintf('2-D embedding has loss %g, and 3-D embedding has loss %g.\n',loss,loss2)

2-D embedding has loss 0.12929, and 3-D embedding has loss 0.0992412.

As expected, the 3-D embedding has lower loss.

View the embeddings. Use RGB colors [1 0 0], [0 1 0], and [0 0 1].

For the 3-D plot, convert the species to numeric values using the categorical command, then convert the numeric values to RGB colors using the sparse function as follows. If v is a vector of positive integers 1, 2, or 3, corresponding to the species data, then the command

sparse(1:numel(v),v,ones(size(v)))

is a sparse matrix whose rows are the RGB colors of the species.

load fisheriris;
rng default; % for reproducibility
[Y,loss] = tsne(meas,'Algorithm','exact');
rng default % for fair comparison
[Y2,loss2] = tsne(meas,'Algorithm','exact','NumDimensions',3);

gscatter(Y(:,1),Y(:,2),species,eye(3))
title('2-D Embedding')

load fisheriris
rng default % for reproducibility
[Y,loss] = tsne(meas,'Algorithm','exact');
rng default % for fair comparison
[Y2,loss2] = tsne(meas,'Algorithm','exact','NumDimensions',3);

figure
v = double(categorical(species));
c = full(sparse(1:numel(v),v,ones(size(v)),numel(v),3));
scatter3(Y2(:,1),Y2(:,2),Y2(:,3),15,c,'filled')
title('3-D Embedding')

fig2plotly(gcf);